MCAT math shortcuts

sin90

1

when the number is the same above and below the divisor it is

1

80/20

cancel the 0's and the answer is 4

cos is

x on the graph

The square root of x is the same as

x^1/2

Ka

x^2/initial molarity

sin is

y on the graph

To find SOHCAHTOA

you look at the angle and its relation to theta

To multiple exponents in scientific notation, you add them

(2x10^4)(4x10^2)-> 8x10^6

cos180

-1

log8 times any number will give .1

-1og8x10^-3-> .1

log3 times any number will give .5

-log3x10^-3--> 2.53

log5 times any number will give .3

-log5x10^-3--> 2.3

cos90

0

sin0

0

sin180

0

1/10

0.1

1/9

0.111

1/8

0.125

1/7

0.143

1/6

0.16

to divide fractions, you multiply by the reciprocal

1/3 / 1/2-> 1/3 x 2/1

How many kilograms are in a gram?

1000 (10kg=10000g)

How many miligrams in a gram?

1000 (10mg=0.01g)

To multiply numbers by 10, you add a 0 or move the decimal place

2.3 x 10 =23 or 23 x 10= 230

To divide numbers by 10 you remove a 0 or move the decimal place to the left

30 /10= 3 or 0.53/1000= 0.00053

To divide exponents in scientific notation, you subtract

3x10^6/6x10^3-> 1/2 x10^3-> 0.5 x10^3-> 5 x10^2

when adding in scientific notation with the same exponent, it does not change

4.7 x 10^-3 + 2.3 x 10^-3 = 7.0 x 10 ^-3

if you want to make the exponent the same, you divide it by 10

5 x 10 ^3/10 -> 50x10^-4

Square is when a number is multiplied by itself

5^2= 25

scientific notation is a shorthand for writing very large or very small numbers

6300-> 6.3 x10^3 or 0.0045-> 4.5 x10^-3

to find the log of a number just look at the 0's

log of 100--> 2

to find the negative log of a number, just look at the exponent

log1x10^-10--> -10

percent

part/whole

SOHCAHTOA

sin=opp/hyp cos=adj/hyp tan=opp/adj

To find square root of scientific notation, you take the square root of the whole number and square root of the power (divide it by 2)

√1x10^-6 -> 1x10^-3

1/5

0.2

1/4

0.25

1/3

0.333

1/2

0.5

cos60

0.5

sin30

0.5

cos45

0.7

sin45

0.7

1/12

0.83

1/11

0.9

cos30

0.9

sin60

0.9

cos0

1

to multiply difficult or complex fraction make the bottom number 100

7/33 x 3/3-> 21/100-> 21%